Converting a short throw video projector to long throw+small diagonal image?

If you put two thin lenses right next to each other, the powers add.

Power in dioptres = 1/focal length in metres, so if you have lenses with focal lengths f1 and f2, the resulting focal length is

f = f1*f2/(f1 + f2)

just like resistors in parallel. So you can make the focal length longer by adding a negative (concave) lens.

Unfortunately you can't change the LCD-to-lens spacing much, so the field angle is more or less fixed. The magnification is thus approximately proportional to the ratio of the image distance to the lens-to-LCD distance. It's a matter of similar triangles--a useful fact from high school optics is that a ray that passes through the centre of a lens is undeviated, so you can easily draw the triangles yourself.

You might be able to get a 1.5:1 improvement or something like that by focusing the projector to its closest setting and picking the right negative lens. That moves the lens further from the LCD, reducing the field angle.

Cheers

Phil Hobbs

That's the case for an intact projector.

Of course if you can make the lens-to-LCD distance larger, you can make the image smaller. Unfortunately it also gets dimmer quadratically as you do that, because most of the light misses the lens. You can fix that by using a lower-NA (numerical aperture) condenser to illuminate the LCD, but then your system starts getting pretty large.

Also at lower NA you don't need nearly such a good lens, so a simple positive lens or achromat would probably work about better than the combination--by applying some large power and then undoing it again, you get the aberrations of two highish-power lenses, whereas with one lens, you get the lower aberrations of the weaker lens. (There are subtleties here, depending on the detailed design of both the projector lens and the negative lens--some of the aberrations will cancel rather than adding, but the net effect will probably be significantly worse.)

Cheers

Phil Hobbs

I'll have another go of setting out, with retort clamps and a mesh as a focussing tool and measurement tool , to get some measurements.. I'd not considered luminance loss, as long as its not more than the gain from keeping a projector as-is and simply reducing the diagonal , increases the luminance in terms of per square inch of the projected image.

Wouldn't it be nice. Unfortunately the loss applies to every point in the image--the reduced field of view is another issue. Consider a single LCD pixel. Light from that pixel expands to fill most of the projection lens (generally not all of it, because otherwise the dimming at the edges of the picture would be worse than it is). Moving the lens further away reduces the angular area (solid angle) quadratically, which dims that one pixel quadratically as well.

You'd be better off with a single large, long-focus achromatic positive lens.

For example:

Cheers

Phil Hobbs